Problem: Simplify the expression. $(6y^{2}-y)(3y^{3}-y^{2}+3y)$
First use the distributive property. $ 6 y^2 (3 y^3) + 6 y^2 (- y^2) + 6 y^2 (3 y) - y (3 y^3) - y (- y^2) - y (3 y) $ Simplify. $ 18y^{5} - 6y^{4} + 18y^{3} - 3y^{4} + 1y^{3} - 3y^{2} $ $18y^{5}-9y^{4}+19y^{3}-3y^{2}$ Identify like terms. $ { 18y^{5}} \color{#DF0030} {- 6y^{4}} {+ 18y^{3}} \color{#DF0030} {- 3y^{4}} {+ 1y^{3}} {- 3y^{2}} $ Add the coefficients. $ { 18y^{5}} \color{#DF0030} { -9y^{4}} {+ 19y^{3}} { -3y^{2}} $